Spatial variation of currents and fields due to localized scatterers in metallic conduction

by R. Landauer

Volume 1 of this journal, thirty-one years ago, included a paper with the above title. Studies of small samples, in recent years, as well as earlier work on disordered samples, have caused some of the content of the earlier work to become widely understood. The aspects stressed in the title, however, relating to the spatial variations in the vicinity of a localized scattering center, have received little attention, except in electromigration theory debates. Here, we return to these aspects of the earlier paper, and emphasize that the transport field associated with a point-defect scattering center is a highly localized dipole field. The nonlinearity of resistance in terms of scattering cross section is discussed. A theory of these effects, which does justice to the coherent multiple-scattering effects present at low temperatures, does not yet exist. Such a theory is likely to modify the effects, but it is unlikely to cause them to disappear. We also discuss closed loops, without leads; the persistent currents expected in these; and a possible method of detecting the persistent currents.